Homework 3
University Astronomy
4/23/10
1
University Astronomy 1017301
Homework Assignment 3
Instructor:
Dr Andrew Robinson
Due Date:
Friday, 16 April 2010.
To tackle some of the following problems you will need to do some research, using either the
textbook or other resources, to find various pieces astronomical data and the values of certain
physical constants. For calculations,
show all your workings in order to receive full credit
.
1.
In an analysis of the spectrum of a star, you measure the wavelength of the H
β
line of
hydrogen to be
λ
=485.3. The rest (laboratory) wavelength is
λ
0
=486.1 nm.
a.
What is the radial velocity of the star relative to Earth?
b.
Is it possible to determine the
speed
of the star? If not, what other information is
necessary?
c.
What would be the
measured
wavelength of the H
α
line (
λ
0
= 656.3 nm)
2.
The absolute
visual magnitude of the Sun is M
V
= 4.82; its apparent
visual magnitude
is m
V
=–26.8. Alkaid, an A1V star, has an absolute magnitude M
V
= –0.59 and
apparent magnitude m
V
=1.86.
a.
What is the luminosity of Alkaid, relative to that of the Sun?
b.
What is the distance to Alkaid, in parsecs?
a) We use the Doppler formula (Lecture 9, slide 27):
Δλ
/
λ
0
= v
r
/c
with
Δλ
= 485.3486.1 = 0.8 nm and
λ
0
= 486.1 nm.
Thus v
r
= c
Δλ
/
λ
0
= 494 km/s.
b) The Doppler shift only tells us the radial velocity – the component
of the star’s velocity in our direction. In order to determine the
speed
, we also need to know the tangential component perpendicular
to our lineofsight, v
t
. In principle we could get v
t
from the star’s
proper motion, but we don’t have this information, so we can’t
determine the speed in this case.
c) We have determined v
r
from the Doppler shift in the H
β
line. We
can now use this to get the Doppler shift in H
α
:
Δλ
=
λ
0
(v
r
/c), where
λ
0
= 656.3 nm. Using v
r
= 494 km/s, we get
Δλ
= 1.08 nm, hence
since
Δλ
=
λ

λ
0
, =655.2 nm
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Homework 3
University Astronomy
4/23/10
2
3.
Find the following stars using the
StarGazer
program. Click on the star to display the
Info panel, and record the name, spectral type, distance in parsecs, absolute magnitude
and surface temperature in a table. Using this information, estimate or calculate the
following additional properties for each star:
a.
What (if any) absorption lines would you expect to find in the spectrum of the star
(see Table 151 in the textbook, or the similar table in the lecture 10)?
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 Spring '10
 DrAndrewRobinson
 Astronomy, absolute magnitude, University Astronomy, molecular cloud core

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